Numerical Generation of Entropies

Abstract

The spurious numerical generation and/or destruction of various types of entropies in models is investigated. It is shown that entropy s? of dry matter tends to be generated if potential temperature is advected by a damping scheme. There is no mean tendency of entropy if the reversible leapfrog scheme is used. Generalized entropies can be assigned to conserved quantities. In particular, the generalized entropy s? of the vorticity of two-dimensional nondivergent flow is shown to grow in presence of irreversible diffusive processes. This entropy increases numerically if the vorticity equation is integrated with an upstream scheme. There are weak oscillations of s? if a leapfrog time step is combined with the Arakawa scheme. Similar results are obtained for an entropy sp related to potential vorticity. Information entropy provides a gross measure of the information contained in ensemble forecasts. It is shown that information entropy decreases spuriously if schemes are used that are contracting in phase space. It is argued that the evaluation of entropies provides a useful check of the quality of numerical schemes.